nginx can help you if you have a lot of slow clients (like mobile devices)
nginx will be like a very fast client for scripts on litespeed - litepseed will be able to send data to the nginx very fast and your script will finish faster too. + you can cache some data with nginx

ive 4 x litespeed webservers behind a pair of LVS loadbalancers, which is behind a cdn
seems to work nicely, is a nice feeling when your gigabit uplink is the bottleneck

ive always been a little confused as to why i'd setup a cluster of servers, then bottleneck all my ssl connections at the loadbalancer. i like lvs because it need not care about the data, it just tunnels tcp connections. each server is handling ssl, distributing the load is the point isnt it

in the end i dont think theres really much difference between loadbalancers. your choice is all about the features you feel are important

i've found HAproxy to be rather poor performance when you need to do sticky sessions
Varnish is great, but doesn't support SSL (last i checked). i use it where i need to enforce caching
Squid is super slow, don't even bother
nxinx i haven't used since the documentation was in russian.
and i've yet to test litespeed's loadbalancer, mostly cause ive already got a solution that works